1. Lecture 4
Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place.

2. Today’s lecture Block 1 Block 2 Block 3 Mole Balances
Size CSTRs and PFRs given –rA=f(X)
Block 2
Rate Laws
Reaction Orders
Arrhenius Equation
Block 3
Stoichiometry
Stoichiometric Table
Definitions of Concentration
Calculate the Equilibrium Conversion, Xe

3. Reactor Mole Balances in terms of conversion
Differential
Algebraic
Integral
Batch X t
CSTR
PFR
PBR X W

4. Last Lecture Relative Rates of Reaction

5. Last Lecture Rate Laws - Power Law Model
A reactor follows an elementary rate law if the reaction orders just happens to agree with the stoichiometric coefficients for the reaction as written.
e.g. If the above reaction follows an elementary rate law
2nd order in A, 1st order in B, overall third order

6. Last Lecture Arrhenius Equation
k is the specific reaction rate (constant) and is given by the Arrhenius Equation.
Where: k T

7. Reaction Engineering Mole Balance Rate Laws Stoichiometry
These topics build upon one another

8. How to find Step 1: Rate Law Step 2: Stoichiometry
Step 3: Combine to get

9. We shall set up Stoichiometry Tables using species A as our basis of calculation in the following reaction. We will use the stochiometric tables to express the concentration as a function of conversion. We will combine Ci = f(X) with the appropriate rate law to obtain -rA = f(X).
A is the limiting Reactant.

10. For every mole of A that react, b/a moles of B react
For every mole of A that react, b/a moles of B react. Therefore moles of B remaining:
Let ΘB = NB0/NA0
Then:

11. Batch System Stoichiometry Table
Species
Symbol
Initial
Change
Remaining A
NA0
-NA0X
NA=NA0(1-X) B
NB0=NA0ΘB
-b/aNA0X
NB=NA0(ΘB-b/aX) C
NC0=NA0ΘC
+c/aNA0X
NC=NA0(ΘC+c/aX) D
ND0=NA0ΘD
+d/aNA0X
ND=NA0(ΘD+d/aX)
Inert I
NI0=NA0ΘI
NI=NA0ΘI
FT0
NT=NT0+δNA0X
and
Where:
δ = change in total number of mol per mol A reacted

12. if a gas phase reaction occurs in a rigid (e.g. steel) batch reactor
Constant Volume Batch
Note: If the reaction occurs in the liquid phase or
if a gas phase reaction occurs in a rigid (e.g. steel) batch reactor
Then
etc.

13. Stoichiometry
Suppose
Batch:
Equimolar feed:
Stoichiometric feed:

14. Constant Volume Batch Reactor (BR)if
then
Constant Volume Batch
and we have

15. Calculating the equilibrium conversion for gas phase reaction,Xe
BR Example
Calculating the equilibrium conversion for gas phase reaction,Xe
Consider the following elementary reaction with KC=20 dm3/mol and CA0=0.2 mol/dm3.
Xe’ for both a batch reactor and a flow reactor.

16. BR Example
Calculate Xe
Step 1:
Step 2: rate law,

17. BR Example Calculate Xe Totals: NT0=NA0 NT=NA0 -NA0 X/2
Symbol
Initial
Change
Remaining A
NA0
-NA0X
NA0(1-X) B
½ NA0X
NA0 X/2
Totals:
NT0=NA0
NT=NA0 -NA0 X/2
@ equilibrium: -rA=0

18. Calculating the equilibrium conversion for gas phase reaction
BR Example
Calculating the equilibrium conversion for gas phase reaction
Solution:
At equilibrium
Stoichiometry
Constant volume
Batch
Species
Initial
Change
Remaining A
NA0
-NA0X
NA=NA0(1-X) B
+NA0X/2
NB=NA0X/2
NT0=NA0
NT=NA0-NA0X/2

19. BR Example Xeb

20. Flow System Stochiometric Table
Species
Symbol
Reactor Feed
Change
Reactor Effluent A
FA0
-FA0X
FA=FA0(1-X) B
FB0=FA0ΘB
-b/aFA0X
FB=FA0(ΘB-b/aX)
Where:

21. Flow System Stochiometric Table
Species
Symbol
Reactor Feed
Change
Reactor Effluent C
FC0=FA0ΘC
+c/aFA0X
FC=FA0(ΘC+c/aX) D
FD0=FA0ΘD
+d/aFA0X
FD=FA0(ΘD+d/aX)
Inert I
FI0=A0ΘI
FI=FA0ΘI
FT0
FT=FT0+δFA0X
Where:
and
Concentration – Flow System

22. Flow System Stochiometric Table
Species
Symbol
Reactor Feed
Change
Reactor Effluent A
FA0
-FA0X
FA=FA0(1-X) B
FB0=FA0ΘB
-b/aFA0X
FB=FA0(ΘB-b/aX) C
FC0=FA0ΘC
+c/aFA0X
FC=FA0(ΘC+c/aX) D
FD0=FA0ΘD
+d/aFA0X
FD=FA0(ΘD+d/aX)
Inert I
FI0=FA0ΘI
FI=FA0ΘI
FT0
FT=FT0+δFA0X
Where:
and
Concentration – Flow System

23. We will consider CA and CB for gas phase reactions in the next lecture
Concentration Flow System:
Liquid Phase Flow System:
Flow Liquid Phase
etc.
We will consider CA and CB for gas phase reactions in the next lecture

24. Heat Effects
Isothermal Design
Stoichiometry
Rate Laws
Mole Balance

25. End of Lecture 4